Problem: Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{n^2 - 4}{n^2 - 7n + 10}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{n^2 - 4}{n^2 - 7n + 10} = \dfrac{(n + 2)(n - 2)}{(n - 5)(n - 2)} $ Notice that the term $(n - 2)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(n - 2)$ gives: $p = \dfrac{n + 2}{n - 5}$ Since we divided by $(n - 2)$, $n \neq 2$. $p = \dfrac{n + 2}{n - 5}; \space n \neq 2$